Heat exchangers are important facilities that are widely used in heating, ventilating, and air conditioning (HVAC) systems. For example, heat exchangers are the primary units used in the design of the heat transfer loops of cooling systems for data centers. The performance of a heat exchanger strongly influences the thermal performance of the entire cooling system. The prediction of transient phenomenon of heat exchangers is of increasing interest in many application areas. In this work, a dynamic thermal model for a cross flow heat exchanger is solved numerically in order to predict the transient response under step changes in the fluid mass flow rate and the fluid inlet temperature. Transient responses of both the primary and secondary fluid outlet temperatures are characterized under different scenarios, including fluid mass flow rate change and a combination of changes in the fluid inlet temperature and the mass flow rate. In the ε-NTU (number of transfer units) method, the minimum capacity, denoted by Cmin, is the smaller of Ch and Cc. Due to a mass flow rate change, Cmin may vary from one fluid to another fluid. The numerical procedure and transient response regarding the case of varying Cmin are investigated in detail in this study. A review and comparison of several journal articles related to the similar topic are performed. Several sets of data available in the literatures which are in error are studied and analyzed in detail.